Classification of Lie bialgebras over current algebras

TL;DR

This paper classifies Lie bialgebra structures on current algebras derived from simple finite-dimensional Lie algebras, expanding understanding of their algebraic properties.

Contribution

It provides a comprehensive classification of Lie bialgebra structures on current algebras g[[u]] and g[u], a previously less understood area.

Findings

Complete classification of Lie bialgebra structures on g[[u]] and g[u]

Identification of new algebraic properties of current algebras

Extension of known classifications to new algebraic contexts

Abstract

In the present paper we present a classification of Lie bialgebra structures on Lie algebras of type g[[u]] and g[u], where g is a simple finite dimensional Lie algebra.